Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 8x + 3$ and $ JT = 3x + 8$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {8x + 3} = {3x + 8}$ Solve for $x$ $ 5x = 5$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 8({1}) + 3$ $ JT = 3({1}) + 8$ $ CJ = 8 + 3$ $ JT = 3 + 8$ $ CJ = 11$ $ JT = 11$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {11} + {11}$ $ CT = 22$